Ministers have allowed successive welfare-to-work schemes worth nearly £1bn to remain open to possible fraud by private companies, a powerful committee of MPs has said.

The Commons public accounts committee said the Department for Work and Pensions failed to ensure that employees of such firms do not defraud the public purse while claiming to place unemployed people into work.

In a report on Friday, MPs also found the government has been unable to ensure that the latest welfare-to-work scheme, the work programme, is entirely free from fraud despite fresh safeguards.

Margaret Hodge, the Labour chair and MP for Barking, said arrangements for overseeing and inspecting contractors were so weak that vital evidence on potential fraud and improper practice was not picked up.

"The department failed to obtain from A4e damning internal audit reports produced in 2009 which pointed to instances of potential fraud and malpractice across the country," she said.

The 34-page internal audit identified dozens of incidents of potential fraud, reputational risk or suspected rule breaking by staff in at least 12 of the company's offices where public money was claimed for placing long-term unemployed people into work.

In one paragraph, auditors said the number of damaging incidents was so large that the company was open to claims of a "systematic failure" to stop the risks of fraud.

Hodge said: the department had been forced to follow up allegations brought to the committee's attention after MPs heard evidence from whistleblowers who alleged that private companies were at the centre of fraudulent activity.

"If it had not been for whistleblowers, a range of systemic issues would not have been identified. The department might have identified these issues if it had asked the right questions of providers," she said.

In the specific case of A4e, whose former head Emma Harrison was a close adviser to David Cameron, the department has yet to assess if the company is "fit and proper" to be paid millions in public money, MPs said.

Eight people have been arrested at the company over allegations of fraud relating to offices in Slough, Berkshire.

Richard Bacon, the Conservative MP for South Norfolk and a committee member, said the DWP adopted a "black box" approach to the work programme, focusing on results without taking proper interest in how they were achieved.

"It's hardly surprising that this vague and hazy approach to financial control and oversight has produced so many questions over proper governance, audit and transparency," he said.

The report follows a serious of fractious committee meetings to discuss the problems of possible fraud in the sector.

Some MPs on the committee are privately angry that the report has been watered down by Conservative members who do not wish to criticise a scheme crucial to government policy.

The work and pensions secretary, Iain Duncan Smith, said in a statement that he had been so concerned about the problems he had written to former Labour ministers – including Hodge – for permission to release papers from their time in office relating to the fraud allegations.

"No such permission has been granted; indeed, some have not replied at all," he said.

A spokeswoman for A4e said that the DWP has identified no evidence of fraud, systemic or otherwise, in relation to any audit of the contracts held with A4e.

"A4e is a different company from the one it was two years ago," she said. "Together with the findings of audits earlier this year by the DWP and the Skills Funding Agency, and with further reviews by the Welsh and Northern Ireland governments, A4e's business has been thoroughly and extensively examined by external auditors."